We have tested the plugin in WP Multisite environment without any problem.
The plugin can be activated either per site basis or using network activate. Both activation works properly.
After the plugin activation the “Product Tabs” menu item appears, tab types can be created for every site, and tab content can be entered for the products on all sites.
Please delete your plugin directory on your server. Download the latest version from My Account menu of webshoplogic.com, and install it again. Maybe the Lite version is installed now on your site.
You should not activate the License, because you have an earlier variant of the plugin.
I hope this will solve the problem.